To Vent Or Not To Vent...

I would like to know which of the following 2 alternatives has a better chance of working.

I have a 6x5 1st floor closet that I want to put a toilet and a sink in to make into a powder room. I have hot and cold water directly underneath. My only issue is the drain/stack.

At 9â€™6â€ from where I want to put the toilet, there's a roof vented 3" PVC drain/stack running vertically in a nearby wall from a 2nd floor bathroom and laundry room. As soon as this drain/stack gets to the basement through the 1st floor, there are 2 - 45 degree turns and the 3â€ PVC slopes slightly downward to the 4â€ main drain. Because of some ducting in the way, it will be difficult (but not impossible â€“ it would have a lot of turns) to tie the new toilet to this drain.

The other choice is 30â€™ away just about where the main drain leaves the house. Itâ€™s a straight run that I can pitch at any angle, even having a vertical drop or an angular drop to a wye where it meets the main drain. I would run 4â€ PVC from the new toilet to the 4â€ main drain. The nearest vent to the intersection of where the 4â€ pipes would meet is 12â€™ â€œupstreamâ€ where there is another 3â€ PVC drain stack running to the other 2nd floor bathroom and is vented to the roof.